I would highly recommend you learn how to properly shoot a DA trigger, with a straight-through pull, especially with a defensive-oriented gun like the 642. You likely won't get the chance to stage your trigger in a defensive encounter, so it's better to learn how to pull the trigger straight-through before you need to (and hopefully you'll never need to).

Get some snap caps (if you don't have them already), and spend a few minutes a day dry-firing. The key is to pull the trigger as quickly as you can while also pulling smoothly and steadily (no starts and stops, no hesitations). Start slow, focusing on smooth and steady, then as you get the hang of it increase the speed. Pulling the trigger faster, while maintaining smoothness and steadiness, will disturb the sights less than pulling slowly and/or with hesitations. Also, it's perfectly acceptable to let your finger slide across the trigger face as you pull, so long as you pull the trigger straight back.

Paying attention to the trigger return/reset is also important. Ideally, your trigger pull and reset will be at the same speed. With time, you can develop a smooth rhythm when firing quickly that will help keep your shots on target.

It takes some practice, but once you do I think you'll find you'll be able to get more of a surprise break with a straight-through pull, which will help you shoot accurately. I used to stage my trigger like you, but once I got the hang of DA shooting I found that a straight-through pull helped me be more accurate more consistently.

Just my opinion.